# Accuracy of maximum likelihood estimates of a two-state model in single-molecule FRET

## Abstract

Photon sequences from single-molecule Förster resonance energy transfer (FRET) experiments can be analyzed using a maximum likelihood method. Parameters of the underlying kinetic model (FRET efficiencies of the states and transition rates between conformational states) are obtained by maximizing the appropriate likelihood function. In addition, the errors (uncertainties) of the extracted parameters can be obtained from the curvature of the likelihood function at the maximum. We study the standard deviations of the parameters of a two-state model obtained from photon sequences with recorded colors and arrival times. The standard deviations can be obtained analytically in a special case when the FRET efficiencies of the states are 0 and 1 and in the limiting cases of fast and slow conformational dynamics. These results are compared with the results of numerical simulations. The accuracy and, therefore, the ability to predict model parameters depend on how fast the transition rates are compared to the photon count rate. In the limit of slow transitions, the key parameters that determine the accuracy are the number of transitions between the states and the number of independent photon sequences. In the fast transition limit, the accuracy is determined by the small fraction of photons that are correlatedmore »

- Authors:

- Laboratory of Chemical Physics, National Institute of Diabetes and Digestive and Kidney Diseases, National Institutes of Health, Bethesda, Maryland 20892 (United States)

- Publication Date:

- OSTI Identifier:
- 22416000

- Resource Type:
- Journal Article

- Resource Relation:
- Journal Name: Journal of Chemical Physics; Journal Volume: 142; Journal Issue: 3; Other Information: (c) 2015 U.S. Government; Country of input: International Atomic Energy Agency (IAEA)

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 37 INORGANIC, ORGANIC, PHYSICAL AND ANALYTICAL CHEMISTRY; ACCURACY; COLOR; COMPARATIVE EVALUATIONS; COMPUTERIZED SIMULATION; EFFICIENCY; ENERGY TRANSFER; ERRORS; FUNCTIONS; MAXIMUM-LIKELIHOOD FIT; MOLECULES; PHOTONS; RELAXATION; RESONANCE

### Citation Formats

```
Gopich, Irina V.
```*Accuracy of maximum likelihood estimates of a two-state model in single-molecule FRET*. United States: N. p., 2015.
Web. doi:10.1063/1.4904381.

```
Gopich, Irina V.
```*Accuracy of maximum likelihood estimates of a two-state model in single-molecule FRET*. United States. doi:10.1063/1.4904381.

```
Gopich, Irina V. Wed .
"Accuracy of maximum likelihood estimates of a two-state model in single-molecule FRET". United States.
doi:10.1063/1.4904381.
```

```
@article{osti_22416000,
```

title = {Accuracy of maximum likelihood estimates of a two-state model in single-molecule FRET},

author = {Gopich, Irina V.},

abstractNote = {Photon sequences from single-molecule Förster resonance energy transfer (FRET) experiments can be analyzed using a maximum likelihood method. Parameters of the underlying kinetic model (FRET efficiencies of the states and transition rates between conformational states) are obtained by maximizing the appropriate likelihood function. In addition, the errors (uncertainties) of the extracted parameters can be obtained from the curvature of the likelihood function at the maximum. We study the standard deviations of the parameters of a two-state model obtained from photon sequences with recorded colors and arrival times. The standard deviations can be obtained analytically in a special case when the FRET efficiencies of the states are 0 and 1 and in the limiting cases of fast and slow conformational dynamics. These results are compared with the results of numerical simulations. The accuracy and, therefore, the ability to predict model parameters depend on how fast the transition rates are compared to the photon count rate. In the limit of slow transitions, the key parameters that determine the accuracy are the number of transitions between the states and the number of independent photon sequences. In the fast transition limit, the accuracy is determined by the small fraction of photons that are correlated with their neighbors. The relative standard deviation of the relaxation rate has a “chevron” shape as a function of the transition rate in the log-log scale. The location of the minimum of this function dramatically depends on how well the FRET efficiencies of the states are separated.},

doi = {10.1063/1.4904381},

journal = {Journal of Chemical Physics},

number = 3,

volume = 142,

place = {United States},

year = {Wed Jan 21 00:00:00 EST 2015},

month = {Wed Jan 21 00:00:00 EST 2015}

}